Statistical Mechanics of Voting

David A. Meyer and Thad A. Brown
Phys. Rev. Lett. 81, 1718 – Published 24 August 1998
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Abstract

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as “chaotic.” We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one-dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We compute the expected complexity of a voting rule and the degree of cohesion/diversity among agents using random matrix models—ensembles of statistical mechanics models—in some representative cases.

  • Received 20 March 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.1718

©1998 American Physical Society

Authors & Affiliations

David A. Meyer1,2,* and Thad A. Brown1,3,†

  • 1Center for Social Computation/Institute for Physical Sciences, Los Alamos, New Mexico
  • 2Project in Geometry and Physics, Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112
  • 3Department of Political Science, 113 Professional Building, University of Missouri/Columbia, Columbia, Missouri 65211

  • *Email address: dmeyer@chonji.ucsd.edu
  • Email address: polstab@showme.missouri.edu

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Vol. 81, Iss. 8 — 24 August 1998

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